Melissa has a gerbil that lives in a cage in the shape of a rectangular prism. She wants to put a ramp in the cage to give her gerbil exercise. The cage has a length of 70 cm, a width of 35 cm, and a height of 50 cm. How long does the ramp need to be to fit diagonally in the cage? Round the answer to the nearest tenth.(1 point)
Responses
60.2 cm
60.2 cm
92.9 cm
92.9 cm
116.3 cm
116.3 cm
78.6 cm
To find the length of the ramp needed, we can use the Pythagorean theorem. The ramp, the length, and the height of the cage form a right triangle.
Let's call the length of the ramp "x". The height of the cage is 50 cm and the width of the cage is 35 cm.
Using the Pythagorean theorem, we have:
x^2 = 50^2 + 35^2
x^2 = 2500 + 1225
x^2 = 3725
x = √3725
x ≈ 60.98 cm
Rounded to the nearest tenth, the length of the ramp needed is 61.0 cm.
Therefore, the closest answer from the available options is 60.2 cm.
So the correct answer is:
60.2 cm